Question

How much does a watch lose per day, if its hands coincide every 64 minutes? 

• A. 32 $\frac{8}{11}$ min
• B. 36 $\frac{5}{11}$ min
• C. 90 min
• D. 96 min
• E.

Hint:

For time-based problems, focus on the discrepancy per cycle, then calculate how it adds up over time.

Answer 1

The Correct Option is A

Step 1: An accurate clock's hands coincide every \( \frac{720}{11} = 65\frac{5}{11} \) minutes.

Step 2: This watch coincides every 64 minutes, so its rate versus a true clock is \( \frac{65\frac{5}{11}}{64} = \frac{45}{44} \).

Step 3: In 1440 true minutes (24 hours), the watch shows \( 1440 \times \frac{45}{44} = 1472\frac{8}{11} \) minutes.

Step 4: The difference is \( 1472\frac{8}{11} - 1440 = 32\frac{8}{11} \) minutes.
\[ \boxed{32\frac{8}{11} \text{ min}} \]